Europe's markets are showing the first signs of an economic recovery, but while Asia will likely be stronger, no region is likely to see robust growth, the CEO of Deutsche Post DHL told CNBC.

"We believe that 2014 [will be] definitely better than 2013, but [there] will not be a massive recovery anywhere," Frank Appel, the company's CEO, told CNBC.

"[This] huge growth we have seen in the last 10-15 years is over," he added, citing a higher base of comparison. "The growth [increase] will be smaller and more modest."

Package delivery and logistics companies, such as DHL, are often viewed as providing early barometers of global economic activity as they are among the first to see changes in demand from businesses and consumers.

Frank Appel, CEO of Deutsche Post DHL, in one of his company's carbon-neutral mail delivery vehicles

Asia is likely to carry the flag of more of the world's economic growth, especially as intra-Asia trade accelerates, he said.

"The wealth creation which will take place in the next 10 years in Asia [will be] still phenomenal," he said, adding his company expects the region will have more than 500 million people achieving middle-class status.

"They need products, they need trade," he said. "The percentage point growth rate will definitely be smaller, but the absolute [number] will still be massive and creates opportunities for companies like us," he said.

Emerging markets, including Asia, will be key growth drivers for Deutsche Post DHL, he said. Asia accounts for about 20 percent of DHL's global sales and the company's strategic plan calls that to rise to 30 percent by 2020.

Appel believes Europe's economy is just beginning to recover.

"We will see a good year in Europe this year. Next year, we will be better," he said, but he cautioned that Europe's path to full recovery will likely be slow.

"If the governments continue to really make [the] good reforms that they started, I think Europe will become significantly more competitive than ever," he said.

"All 30 years of budget deficits were slowly created over the years. It takes five to 10 years really to get back," Appel said. "My home country, Germany, is a good example. It was not overnight, but the reforms really made Germany more competitive and [a quick recovery] will not be the case for Europe either," he added.